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4h
comment References on a game with white and black stones
I've been working here and there on this since you posted it; there's definitely some interesting patterns, but I don't yet have a complete collection of conjectures. I'll probably give up and post my partial results by the end of another week. Where did you come across this game? Or is it your own invention?
16h
comment How do the roots of “$x^2 + bx + c$” change as $b$ is kept constant and $c$ is changed?
@Michelle Consider similar situations with numbers. $\sqrt{3}=\sqrt{|3|}$, since $3>0$. And $\sqrt{-2}=i\sqrt{2}=i\sqrt{|-2|}$ since $-2<0$. So any square root of a real number is related to the square root of its absolute value, possibly with a factor of $i$. Using this same idea, I figured that introducing $\sqrt{\left|b^2-4ac\right|}$ would help in understanding. To avoid having to write something like $s/2$ all the time, I defined $s$ to be $\frac12\sqrt{\left|b^2-4ac\right|}$. Incidentally, "exploratory algebra" was not a typo. There are many different choices you can make when exploring.
2d
comment Converting programming logic to mathematical notation
@BugHunterUK, "how to write algorithms in math": as Ian said, pseudocode is fairly common. You can find examples in many papers/books on algorithms in graph theory, for instance. "express solutions to problems in math": Most solutions to problems in math are not algorithms. And when they're close to code, they're often closer to code in a pure functional language than a procedural language.
Feb
5
comment How to define “being inside of something” in the context of topology?
@holistic, convex hulls come from "computational geomtery", although they can sometimes be closely tied to "linear algebra". For time, you may want to say something like "as time increases from 0 to 1, the percentage of the volume of the apple that is a subset of the convex hull of the bag increases from 0 to 1".
Feb
5
comment mathematical symbol for a new member replacing a member in a set
This contains the answer I was thinking of writing, but is twice as well-written as mine woild have been. Nice job!
Feb
5
comment How to define “being inside of something” in the context of topology?
The kinds of examples of being inside you refer to are not really places for topology to shine. Homeomorphism, the concept of "these are the same as far as topology is concerned" does not preserve things like "food being in a shopping bag" (though arguably "food touching a shopping bag"). If you're looking for a mathematical idea that's not necessarily from Topology, perhaps "inside" is close to "is a subset of the convex hull", but that's a geometric concept, not a topological one.
Feb
4
comment Converting programming logic to mathematical notation
It's a common error, but "discreet" and "discrete" have very different meanings. I suspect your example isn't something that's going to have an interesting mathematical translation. In math there's a lot of pseudocode and proofs of things like "checking up to sqrt(n) is enough". It's not like there's a separate mathematical way to write every algorithm (aside from I guess writing it in a functional language)
Jan
28
comment General clarification for derivative notation
@AlanL, did this answer your question? If so, you may want to accept it. If not, let me know if anything I said is unclear or if there's some aspect of the question I did not address.
Jan
28
comment Sharing a pepperoni pizza with your worst enemy
I am now hesitant to split a pizza with you.
Jan
27
comment discrete mathematic Question that i need help with please
Try to use Stars and Bars as described at en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29 (or some other technique from your textbook/class notes, if applicable) and post your thoughts and attempts.
Jan
25
comment Placing stones on vertices of polygon
@MJD Nice exposition in that blog post! If you're not familiar with Octal Periodicity, you may want to see page 11 in these notes to see how to confirm that the Nim values for "rows of dots" are eventually periodic.
Jan
24
comment How do the roots of “$x^2 + bx + c$” change as $b$ is kept constant and $c$ is changed?
@G.Sassatelli I think there's a bit more that could be said about the dynamic geometry that may not be immediately obvious to someone upon first looking at that formula; see my answer for what I have in mind.
Jan
23
comment What is the fastest way to multiply two digit numbers?
Something like the book Secrets of Mental Math might help you. Also, there are few enough pairs of two-digit numbers that if you really want to you could memorize all the products (maybe easier with some phonetic mnemonics or something).
Jan
23
comment Are there any online math games similar to CheckIO or CodeCombat?
"Human Resource Machine" is a computer game with programming puzzles in a sequence of quite-constrained assembly-like languages. Some of the programming challenges are related to things in mathematics like the fibonacci sequence.
Jan
23
comment Why does an argument similiar to 0.999…=1 show 999…=-1?
What do you mean by $\mathbb{Q}_{10}$? I would think it wouldn't be defined because $\mathbb{Z}_{10}$ has zero divisors.
Jan
23
comment Limits Outside of Mathematics.
Continuously compounded interest? A motivation for the concept of derivative which comes up in tons of scientific models? What sort of answer are you looking for?
Jan
18
comment Definition of topological space: Is Ω equal to the powerset of X?
@leftaroundabout The indiscrete/trivial topology also is in some sense "behaving as a plain old set". Both are adjoints to the forgetful functor that forgets about topological structure: ncatlab.org/nlab/show/discrete+and+codiscrete+topology
Jan
16
comment Why are sets like $\{x \in \mathbb{Q}|-\pi < x < \pi\}$ both closed and open in $\mathbb{Q}$?
@FemaleTank, There are two different topologies being discussed. One is "balls contain all the real numbers they should", but the other, the one in which the set is both open and closed, is "we only include the rational numbers in any considerations".
Jan
16
comment Notation of the second derivative - Where does the d go?
@IwillnotexistIdonotexist First, it destroys the nice "multiplication" of factors of the form $\frac{\partial}{\partial x}$ by saying something like "$\partial\partial=\partial^2$ on top, but $(\partial x)(\partial y)=\partial xy$ on bottom". More importantly, IMO, is the fact that, in general: $\frac{\partial}{\partial x}$ and $\frac{\partial}{\partial y}$ don't commute, but $x$ and $y$ do. So to use the notation you proposed would require that $\partial xy$ in a denominator can't be replaced with $\partial yx$, even though in all other real-anaylsis contexts $xy\to yx$ would be fine.
Jan
16
comment Notation of the second derivative - Where does the d go?
@IwillnotexistIdonotexist I don't think I've seen a multivariable calculus book that does that. I've only seen books write things like $\partial x\partial y$ in the denominator, and I believe for good reason.